To determine the probability of spinning specific numbers in two spins, we need to follow these steps:
1. Probability of the first event (spinning a 3):
- Since the spinner has 8 evenly divided regions, each numbered from 1 to 8, the probability of landing on any specific number in one spin is [tex]\(\frac{1}{8}\)[/tex]. Therefore, the probability of spinning a 3 on the first spin is [tex]\(\frac{1}{8}\)[/tex].
2. Probability of the second event (spinning a 5 after the first spin was a 3):
- The second spin is independent of the first spin, meaning the outcome of the first spin does not affect the second. Thus, the probability of spinning a 5 on the second spin is also [tex]\(\frac{1}{8}\)[/tex].
3. Combined probability of both events occurring in sequence:
- To find the probability of both events happening (first spinning a 3 and then spinning a 5), we multiply the probabilities of each independent event:
[tex]\[
\text{Probability of getting a 3 and then a 5} = \left(\frac{1}{8}\right) \times \left(\frac{1}{8}\right)
\][/tex]
- Calculating this gives:
[tex]\[
\frac{1}{8} \times \frac{1}{8} = \frac{1}{64}
\][/tex]
Therefore, the probability that the first number is a 3 and the second is a 5 is [tex]\(\frac{1}{64}\)[/tex], which corresponds to option C.
